assistant professor, smaranda cimpoeru, phd e-mail ...ecocyb.ase.ro/nr20152/05 -...

Assistant professor, Smaranda CIMPOERU, PhD

E-mail: [email protected]

The Bucharest University of Economic Studies

USING SELF-ORGANIZING MAPS FOR ASSESSING SYSTEMIC

RISK. EVIDENCES FROM THE GLOBAL ECONOMIC CRISIS

Abstract. The importance of correctly assessing systemic risk has

increased substantially after the events from 2007. A wide set of parametric and

non-parametric methods has been used to address the problem and identify the

leading risk factors for potential crisis situations. Out of these, the class of neural

networks represented by self-organizing maps has become an important technique

but only with a modest usage for the economic crisis. We apply the self-organizing

maps technique for a set of worlds’ economies, with the goal of identifying the

resemblances and differences between worlds’ economies. The model developed on

self-organizing maps ensures detection of the imbalances and vulnerabilities of

economies and find the determinant variables (early warning signals) for a

financial-economic crisis situation. The study has the advantage of including in the

analysis a pre-crisis and a post-crisis assessment, gaining much insight from the

structural changes produced in the topology of the economies.

Keywords: Self-Organizing Maps, Neural Networks, Early Warning

Systems, Systemic Risk, Global economic crisis.

JEL Classification: C45, H63, C49

1. Introduction

The globalized financial environment that we are experiencing nowadays

creates the premises for the financial instability to be transmitted over the countries

which could lead to a generalized collapse of the real economy. Apparently,

although the stress tests performed on European level gave good results, the credit

ratings for many countries in Europe worsened during 2011. Miricescu (2014)

makes an analysis of the dominant factors that impact the long-term sovereign

rating. In his paper, he highlights the government debt to GDP ratio which raised

for the EU from app. 62% in 2000 to 88% in 2014. In this context, the problem of

finding and evaluating an accurate early warning system for the European financial

system becomes a real challenge and of utmost importance. Many papers have

investigated what were the causes of the crisis. For example, Reinhart and Rogoff

(2008) find the following lead indicators of crisis: real housing and equity prices,

current account deficits, GDP growth, increases in debt.

mailto:[email protected]

Smaranda Cimpoeru

_________________________________________________________________ Recent financial crisis has demonstrate that the economies are vulnerable in front

of the systemic financial distress and that it very important for policy makers to

understand the sources of these vulnerabilities in order to increase the capacity for

absorbing shocks of the financial and economic system. Moreover, the financial

integration which is a very wide phenomena (Moscalu, 2014) leads to significant

linkages across markets, so that a holistic approach of the financial crisis has to be

applied.

Especially after the eruption of the global crisis in 2007, the importance of

understanding and correctly assessing risk factors and risk transmissions within

markets of the economy has risen as a particularity of assessing financial instability

situations. As a general definition (Oet et al, 2010), the early warning systems are

“data-driven approaches” with the goal of identifying variables associated with past

crises and alert policy makers of other potential future crises. Early warning

systems are based on the assumption that crisis factors can be identified before a

crisis and can be used for improving policy measures at macroeconomic level.

Objective of the paper is twofold: identification of resemblances and differences

between different economies of the world in order to detect the imbalances and

adjust the corrective policy as to take into account this disequilibrium; find the

determinant variables (early warning signals) for a financial-economic crisis

situation.

Structure of the paper is as follows. In section 2 we review the specialty literature

of using Self-Organizing maps in the context of the global financial crisis. In

section 3 we introduce the basics of the self-organizing maps (including vector

quantization concept) and in the next section we present briefly the algorithm of

the method. The second part of the paper is dedicated to the case study – we

introduce the database, the variables, the topology of the economies before the

crisis (2007) and the structural mutations that took place in the post-crisis context.

Last section draws the conclusions.

2. Using Self-Organizing Maps for assessing the global financial crisis – Literature review

The main advantage of the neural networks is the fact that they are non-parametric

models that do not require the assumptions for statistical data distribution and are

not limited by linear specifications. Considering that the indicators of a financial

crisis are non-linearly related (Fioramonti, 2008), neural networks were widely

used for evaluating the financial, debt or currency crisis. However, the focus of the

current paper is on the self-organizing maps, as a class of the neural networks

models, so we will provide the literature review of using this technique in assessing

financial stress. Despite the large number of papers that study the use of SOM in

engineering or medicine, the specialty literature is whatsoever scarce in what

concerns the applications of SOM in financial stability and economic crisis

assessment.

Using Self-organizing Maps for Assessing Systemic Risk. Evidences from the

Global Economic Crisis

_________________________________________________________________

First studies that apply SOM to model currency crisis are that of Arciniegas and

Arciniegas Rueda (2009). They explore the correlation between real effects of

speculative attacks on currency and a set of macroeconomic variables. In Sarlin

and Marghescu (2011) we have the same idea, of applying the SOM for the

indicators of a currency crisis. Dattels et al. (2010) develop a Global Financial

Stability Map, by using six composite indices. However, it has the disadvantage

that the sources of individual stress are difficult to identify and, as stated by the

authors, the results are to be viewed as illustrative.

Sarlin, Peltonen (2011) develop a Self-Organizing Financial Stability Map

(SOFSM) which allows the identification of the vulnerability sources and performs

well for out-of-sample systemic financial crisis. For the topologically ordered

SOFSM, the financial stability neighborhood represents the “contagion of

instabilities through similarities in the current macro-financial conditions”. The

map is represented in the following areas of the financial stability cycle: pre-crisis,

crisis, post-crisis and tranquil state. The SOFSM developed performs better than a

logit model for classifying in sample data and for predicting the global crisis from

2007. However, the map does not show the imbalances between different

economies across the world facing the economic crises.

Itturiaga and Sanz (2013) propose a model for detecting and managing divergences

between countries in order to anticipate the danger of a financial crisis. They use

the Self-Organizing Maps model to perform a classification of the European

countries, as well as German and Spanish regions. The reason for choosing these

two countries comes from the similar territorial organization but with the

significantly different financial status. The SOM model is applied to find the extent

to which national financial instability is due to the regional macroeconomic

imbalances. Public expenditure and saving rate are found to be the most critical

variables with impact on a country’s economy.

A worth to mention adaption of the Kohonen standard SOM is the Self-Organizing

Time Map designed by Sarlin (2013a, 2013b) with the purpose of abstraction the

structure in temporal multivariate problems. When ordering ascending of time the

one-dimensional arrays, the SOTM will enable a two-dimensional representation

with the multivariate data structures on the vertical and the temporal direction on

the horizontal. The ordered SOTM can be used for projecting individual or grouped

data onto the map. In Sarlin (2013b), the SOTM is applied to financial stability

surveillance. The results show that high equity prices, current account deficits and

GDP growth are the main triggers for financial crises. The Self-Organizing Time

Maps can be used for: identifying the imbalances in indicators over time, the

structural changes in data, the specific location of univariate and multivariate

changes across the data.

As also it was mentioned in Sarlin, Peltonen (2011), the SOM applied for assessing

financial and economic crisis “enables disentangling the specific threats, risks and

Smaranda Cimpoeru

_________________________________________________________________ triggers, and should be treated as a starting point rather than an ending point for

financial stability analysis”.

3. Self-Organizing Maps – Essentials

Neural networks can be classified in two major classes: supervised and

unsupervised networks. For the supervised ones, a target vector is presented to the

network so that it adjusts the results to the expected output. The unsupervised

networks are assimilated to the exploratory analysis and clustering methods. The

Self-Organizing Map is an unsupervised competitive type of network.

The first scientists to delimitate the notions of brain maps are Mountcastle (1957)

and Hubel and Wiesel (1962). They found that certain neural cells in the brain react

to specific sensorial stimulations. Moreover, the designated cells are grouped in

local assemblies and their location is assigned with the response to a certain

stimulus. This is the way the brain maps, which are nothing less than systems of

cells, have been discovered and defined.

Later on, Merzenich et al. (1983) has reported that the brain maps depend strongly

on sensorial experiences. This idea has developed into the competitively learning

neural networks. This means that in a sequel of cells, the process of cells’

adaptation to the input signal makes them dependent on the specific input

characteristics.

However, the brain maps models which were inspired by biology could not be

applied to data analysis, and this was mainly due to the fact that the resulting maps

were partitioned, meaning that they were made of several patches, between which

the ordering was random and discontinue, so no global order existed over the entire

map.

That is why, in the neural models used in data analysis, controlling the nodes

activities through the neural connections is not enough. There is a need for an extra

control, using factors to intermediate the information without mediating the

activities. This is where the vector quantization comes into place.

The idea of vector quantization (VQ) dates back to 1850 (Dirichlet) and 1907

(Voronoi tessellation in spaces of arbitrary dimensionality). This technology used

in digital signal processing, partitions the vector-values input data into a finite

number of contiguous regions, where each region is represented by the single

model vector or the codebook vector. The VQ is usually illustrated with the

Euclidean distance. For instance, if we consider the input data formed of n-

dimensional Euclidean vectors, denoted by Y and the model vectors denoted by 𝑀𝑖 . We denote with 𝑀𝑤 the winner model vector, the vector with the smallest Euclidean distance from the input vector, Y. Mathematically, we can write:

𝑤 = 𝑎𝑟𝑔 min𝑖

{‖𝑌 − 𝑀𝑖‖} (1)

If we further denote with f(Y) the probability density of Y, the mean quantization

error E is then defined as:

𝐸 = ∫ ‖𝑌 − 𝑀𝑤‖2𝑓(𝑌)𝑑𝑉

𝑉 (2)



_________________________________________________________________

Where dV is a volume differential on the data space V. The objective function, E, is

an energy function which could be minimized by the gradient descent procedure.

(Kohonen, 2013).

The above outlined VQ technique is also called the “k-means clustering” and the

self-organizing map can be viewed as a generalization of the k-means clustering

algorithm. The self-organizing map is first introduced by Kohonen at the beginning

of the 80s. The technique resembles the VQ, but the vector models are spatially and

globally ordered. In Figure 1, we represent a self-organizing map – for an input

vector Y, the feature map finds the winning node in the finite output space. The

associated weight vector give the coordinates of the node from the input space.

As per Kohonen (2013), the input data, Y, is mapped to a set of models (𝑀𝑖) where 𝑀𝑤is the best match for Y. All models that are in the close surrounding of the winner model are better match with Y than the others. The figure illustrates the

basis of the Self-Organizing Maps (SOM) algorithms. Similar models will be

assigned with nodes that are closer in the grid (smaller Euclidean distance in the

VQ), while less similar models will localized further away. The essentials of the

SOM, as stated by Kohonen (2013) is: “Every input data item shall select the

model that matches best with the input item, and this model, as well as a subset of

its spatial neighbors in the grid, shall be modified for better matching”. The

mentioned modification is associated with the winner model. However, due to the

fact thatit is not a single vector that changes, but an entire family of neighbors

vectors, this implies a local ordering of the models in the neighborhood. This local

ordering will propagate across the grid.

Figure 1 – Feature Map – Self Organizing Map representation

Continuous

Input Space

Finite Output

Space

Feature Map

Y Model 𝑀𝑤 with the winning

neuron and the

neighborhood

Smaranda Cimpoeru

_________________________________________________________________ Two algorithms can be used for producing an ordered set of models in the map.

The first one assumes a stepwise procedure, meaning that the input data are

presented to the network one at a time, for as many iterations as necessary to reach

a state of equilibrium. In the second type of algorithm, all input data are presented

to the algorithm as one batch and all the models are modified in a single operation.

The batch process repeats a certain number of times until the exact stabilization of

the models. In the second type of algorithm, the state of equilibrium is attained

faster than in the first one.

4. The Algorithm used for training the Self-Organizing Map

The basic Kohonen network has a layer of input nodes and only one layer of output

neurons. The neurons from the first layer form a discrete topological mapping of an

input space, 𝑌𝜖R𝑛. The algorithm is based on minimizing the distances between the nodes, and as mentioned before on the Vector Quantization idea.

The initial step (step zero) of the training algorithm consists in initializing all

weights of the network {𝑤1, 𝑤2, … , 𝑤𝑀}with small random values. We mention that: 𝑤𝑖 is a weight vector associated with the neuron “i”, having the same dimension, n, as the input vectors; M is the total number of neurons in the input

space and suppose that 𝑙𝑖 is the location of vector “i”on the grid. For the first phase of the algorithm, in the first step an input training vector, Y(t) is

chosen from the input space and presented to the grid. The second step of the

algorithm consists in examining every node of the network and finding the winning

neuron, that is, the neuron having the weight vector closest to the input vector, in

terms of distances (for example, in eq. 3 the Euclidean distance is used):

min 𝑑𝑗(𝑦) = √∑ (𝑦𝑖 − 𝑤𝑗𝑖)2𝑛

𝑖=1 (3)

𝑣(𝑡) = arg min𝑘∈Ω

‖𝑌(𝑡) − 𝑤𝑘(𝑡)‖ (4)

whereΩ is a set of neuron indexes. In the second phase of the algorithm, the weights of the winning neuron and its

neighbors are updated as stated in equations 5 and 6.

𝑤𝑘(𝑡 + 1) = 𝑤𝑘(𝑡) + 𝐿(𝑡)𝑛(𝑣, 𝑘, 𝑡)[𝑌(𝑡) − 𝑤𝑣(𝑡)] (5)

or otherwise stated:

∆𝑤𝑘(𝑡) = 𝐿(𝑡)𝑛(𝑣, 𝑘, 𝑡)[𝑌(𝑡) − 𝑤𝑣(𝑡)] (6)

Where:

𝐿(𝑡)is the learning rate of the network. These coefficients are scalar-valued that decrease monotonically and satisfy the following properties (7):



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0 < 𝐿(𝑡) < 1; lim𝑡→∞

∑ 𝐿(𝑡) → ∞; lim𝑡→∞

∑ 𝐿2(𝑡) < ∞ (7)

𝑛(𝑣, 𝑘, 𝑡) is the neighborhood function, which in practice has the form of a Gaussian function, as in (8):

𝑛(𝑣, 𝑘, 𝑡) = exp [−‖𝑙𝑣−𝑙𝑘‖

2

2𝜎(𝑡)2] (8)

Where 𝑙𝑖 is the location vector of neuron “i” and 𝜎 represents the range or the radius of the neighborhood, which decrease monotonically with time. The Gaussian

function is introduced in the adjusting equation inorder to give lower importance to

the neurons of the neighborhood that are situated further away from the main node

found as the BMU (Best Matching Unit) of the input neuron.

The algorithm is than reiterated from the first step (choosing the input neuron) until

the map converges. The algorithm was presented as stated by Kohonen (2013) and

Yin (2008).

After the convergence of the SOM algorithm, the feature map has important

statistical properties (these are also mentioned in some Lecture Notes from

J.Bullinaria, 2004). First of all, the feature map which consists basically of a set of

weights in the output space offers a good approximation of the input space. This is

exactly the basis of the Vector Quantization theory that we explained in the

previous section and which is the foundation of the dimensionality reduction

process.

Secondly, the feature map is topologically ordered, meaning that the space of a

neuron in the output layer corresponds to a certain partition (feature) of the input

neurons. This is an immediate consequence of the weight update equation (eq. 4),

which is applied to all the nodes of the neighborhood and not only to the winning

neuron. That is why, the map is considered an “elastic” net – as the neuron in one

neighborhood are connected through the correspondents in the input space, than the

network will offer an image that is linked to the topological ordering of each stage

of the network training.

The third property of the feature map refers to the variation in the input

distribution. The regions where training vectors are drawn with high probability of

occurrence will be mapped into wider partitions of the output layer and with a

better resolution. Property three of the feature map will be illustrated in the case

study with the outliers distribution on the network.

The fourth property of the feature map states that the Self-Organizing Maps are

able to select the best features irrespective of the distribution in the input space,

that is they perform very well even for non-linear data. This is a very important

highlight, especially compared to other dimensionality reduction techniques, like

Principal Component Analysis which can be applied only if the data is linear.

Smaranda Cimpoeru

_________________________________________________________________ Otherwise said, the SOM can be viewed as an non-linear generalization of the

Principal Component Analysis, as it offers a solution for finding principal surfaces

or curves.

5. Case study

In the case study, we propose applying the Self-Organizing Map model to a set of

world economies, for two key periods: 2007 – the year before the eruption of the

crisis and 2010, the aftermath of the crisis. The inputs of the network are a set of

macroeconomic variables registered in the two periods. The results of the map are

numerous. First of all we obtain the topology of the economies before the eruption

of the crisis and the structural changes that appeared after the crisis,that is how the

world map changed from an economic point of view. Secondly, we analyze the

distribution of the macroeconomic variables across the countries for the two

periods and find the early warning signals of a crisis.

5.1 Data Base

The Data Base constructed is formed of 15 variables, which are detailed in Table 1.

Data sources include: World Bank, CIA World Fact Book, Eurostat. Decision upon

variables included in analysis follows the specialty literature, like Sarlin and

Peltonen (2011), Iturriaga and Sanz (2013).

Table 1 – Macroeconomic variables included in analysis (source of metadata:

World Bank)

V1 Agriculture, value added (% of GDP)

Agriculture corresponds to ISIC divisions 1-5 and includes forestry,

hunting, and fishing, as well as cultivation of crops and livestock

production.

V2 Cash surplus/deficit (% of GDP)

Cash surplus or deficit is revenue (including grants) minus expense,

minus net acquisition of nonfinancial assets. This cash surplus or deficit

is closest to the earlier overall budget balance.

V3 Domestic credit provided by financial sector (% of GDP)

Domestic credit provided by the financial sector includes all credit to

various sectors on a gross basis, with the exception of credit to the

central government, which is net.

V4 GDP per capita (current US$)

GDP per capita is gross domestic product divided by midyear population.

V5 GDP growth (annual %)

Annual percentage growth rate of GDP at market prices based on



_________________________________________________________________

constant local currency.

V6 Central government debt, total (% of GDP)

Debt is the entire stock of direct government fixed-term contractual

obligations to others outstanding on a particular date.

V7 Gross savings (% of GDP)

Gross savings are calculated as gross national income less total

consumption, plus net transfers.

V8 Industry, value added (% of GDP)

Industry comprises value added in mining, manufacturing (also reported

as a separate subgroup), construction, electricity, water, and gas. Value

added is the net output of a sector after adding up all outputs and

subtracting intermediate inputs.

V9 Inflation, consumer prices (annual %)

Inflation as measured by the consumer price index reflects the annual

percentage change in the cost to the average consumer of acquiring a

basket of goods and services.

V10 Interest rate spread (lending rate minus deposit rate, %)

Interest rate spread is the interest rate charged by banks on loans to

private sector customers minus the interest rate paid by commercial or

similar banks for demand, time, or savings deposits.

V11 Money and quasi money growth (annual %)

Average annual growth rate in money and quasi money. Money and

quasi money is frequently called M2.

V12 Market capitalization of listed companies (% of GDP)

Market capitalization (also known as market value) is the share price

times the number of shares outstanding.

V13 Bank nonperforming loans to total gross loans (%)

Bank nonperforming loans to total gross loans are the value of

nonperforming loans divided by the total value of the loan portfolio

(including nonperforming loans before the deduction of specific loan-

loss provisions).

V14 Stocks traded, total value (% of GDP)

Stocks traded refers to the total value of shares traded during the period.

This indicator complements the market capitalization ratio by showing

whether market size is matched by trading.

V15 Unemployment, total (% of total labor force) (modeled ILO estimate)

Unemployment refers to the share of the labor force that is without work

but available for and seeking employment.

Smaranda Cimpoeru

_________________________________________________________________ The variables from Table 1 are recorded for a sample of 80 countries1, chosen

based on the percentage in global GDP and availability of the data .Although we

identified a set of outliers in the data, we decided to keep the respective economies

in the analysis considering the importance of the respective economies for the

study. We mention that Macedonia, Bosnia and Herzegovina and Armenia are

outliers (upper limit) for unemployment, with the highest values from the series.

The economy of Qatar records an extremely high value for the Value added in

industry, while Norway is situated at the upper limit of the Credit surplus and

Canada at the lower limit of Money growth. On the other hand, Nigeria is situated

at the other extreme, with a very high value for the Money growth and Ukraine at

the upper limit of the rate for Non-performing loans. We will observe that these

outliers will be counted as such also in the construction of the map.

5.2 State of the economies in 2007 determined by the SOM model

Due to lack of data for the entire sample, the variables Government Debt (V6) and

the Interest rate spread (V10) were removed from the list of inputs. We use the

variables registered at 2007 and after applying the algorithm, we obtain the map in

Figure 2. The80 countries from the sample are grouped on 9 regions, three

dominant ones comprising 62 countries out of the total.

We will start by analyzing the first group of countries (center, blue in Figure 3)

which is also the most numerous. The 26 countries can be classified geographically

as follows:

o Latin America: Chile, Bolivia, Peru, Argentina, Mexico, Colombia, Uruguay, Guatemala, El Salvador, Brazil.

1Argentina, Armenia, Australia, Austria, Belarus, Belgium, Bolivia, Bosnia and

Herzegovina, Brazil, Bulgaria, Canada, Chile, China, Colombia, Cote d’Ivoire, Croatia,

Cyprus, Czech Republic, Denmark, Dominican Republic, Egypt, El Salvador, Estonia,

Finland, France, Georgia, Germany, Greece, Guatemala, Hungary, Iceland, India,

Indonesia, Iran, Ireland, Italy, Japan, Jordan, Korea Rep., Latvia, Lithuania, Macedonia

FYR, Malaysia, Malta, Mexico, Moldova, Morocco, Netherlands, New Zealand, Nigeria,

Norway, Oman, Pakistan, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania,

Russian Federation, Saudi Arabia, Serbia, Singapore, Slovak Republic, Slovenia, South

Africa, Spain Sri Lanka, Sweden, Switzerland, Thailand, Trinidad Tobago, Tunisia,

Turkey, Ukraine, United Kingdom, United States, Uruguay, Zambia.



_________________________________________________________________

o Europe: Slovenia, Romania, Czech Rep., Poland, Slovak Rep., Estonia, Lithuania, Portugal, Latvia, Bulgaria, Croatia, Greece,

Hungary, Malta.

o Asia: Indonesia, Turkey. We might say that, from a geographic point of view, there is a predominance from

Central and East European countries and Latin American ones. We will now

analyze the characteristics of the first group of countries. The variables for which

the mean in the group is significantly different (lower in this case) than that of the

entire sample are: market capitalization (V12), Stocks traded (V14), Gross savings

(V7) and GDP/capita (V4). Considering the variables that individualize this group

of countries, we can outline the following traits: capital market insufficiently

developed (stocks traded, market capitalization), low financial power of the

population (GDP/capita and gross saving). After exposing the characteristics for all

the group of countries, we will analyze the position of the neighborhoods on the

map and what important conclusions can be drawn.

Figure 2 – Self-Organizing Map of the economies in 2007

We continue our exposure for the so called clusters with the group on the left (the

red one). The 21 countries included in this group are the following (based on the

geographic criterion):

Smaranda Cimpoeru

_________________________________________________________________ o Europe: Island, Switzerland, Sweden, Finland, UK, Spain,

Denmark, Ireland, Netherlands, Germany, Austria, Belgium, Italy,

Cyprus, France.

o Asia & Australia: Korea, Japan, Australia, New Zeeland. o North America: USA, Canada.

In Figure 3 we have the characteristics of the group. We find that the designated

countries register a value higher than the rest of the economies for the following

variables: GDP/capita (V4), Domestic Credit (V3), Stocks traded (V14), and

Market capitalization (V12). While the variables that register a lower average than

that of the group are: Agriculture value added (V1), Inflation (V9), GDP growth

(V5), Money growth (V11) and Industry value added (V8). We could say that this

is the group of developed economies, with a mature financial market, however

threatened by a stagnation of the economy (GDP growth, Money growth on a

negative path).

We note that in the process of training the map, we used the standardized GDP and

in the figures below, the initial values are presented. The software used was

ViscoverySOMine, with the courtesy of the producers, in the purpose of academic

research.

Figure 3 – Characteristics of the second group of countries

In the left part of the map, we also find two smaller subsets: Jordan and South

Africa (left, lower corner) and Norway plus Singapore (left, upper cornet). Norway

and Singapore are characterized by the highest values for Cash surplus (V2), Gross

Savings (V7) and GDP per capita (V4), while Jordan and South Africa have the

greatest market capitalization. Based on these extremes, it becomes easier to

compare the countries from the red cluster considering their neighbors. We will

return to this issue at the end of the section.

The third group of countries includes the following 15 economies (the yellow

group on the right), classified on the geographical criterion:

o Europe: Serbia, Georgia, Moldova. o Asia: Iran, Belarus, Russia, Pakistan, Sri Lanka. o Africa: Egypt, Tunisia, Zambia, Cote d’Ivoire, Nigeria. o Latin America: Rep. Dominican, Paraguay.



_________________________________________________________________

In Figure 4, we find that the variables with a higher average than that of the entire

sample are: value added in the agriculture (V1), Inflation (V9), Money growth

(V11), while the variables with a lower average than that of the sample are:

Domestic Credit (V3), GDP per capita (V4) and Stocks traded (V14). This could

mean that this group of countries are characterized by a moderate economic

development and a low development of the financial market (Stocks traded,

domestic credit).

Figure 4 – Characteristics of the third group of countries

Still on the right side of the map we find Bosnia and Herzegovina, Macedonia and

Armenia, grouped based on the very high levels for the unemployment in these

economies. We also mention in this side of the map Ukraine, with an extreme high

value for the level of non-performing loans.

The last group of countries (upper side of the map, green) includes the nine

following countries:

- Asia: China, Philippines, Saudi Arabia, Oman, Malaysia, India, Thailand. - Africa: Trinidad and Tobago, Morocco.

This group is individualized by higher values for Gross Savings and Value Added

in Industry, thus could be assimilated to the strongly industrialized countries. In

Figure 5 we have the topology of the 13 variables included in the analysis on the

map of countries – these are the so called U-matrixes.

Figure 5 – Distribution of variables (U-Matrix) at 2007

Smaranda Cimpoeru

_________________________________________________________________

Based on Figure 5 and on the characteristics identified above, we can make a

comparative analysis of the economies before the crisis (2007). Starting from the

left side of the map, we can say that on this side we have concentrated the

developed economies, as shown by the distribution of all macroeconomic variables

(Figure 5). We can say that in 2007, the best situated economies were that of

Sweden, Norway, Finland, USA, Great Britain, Netherlands, Canada. For Japan

and Island, we notice the “red” zones on the Domestic credit, signaling very high

levels of this variable. Ireland, Spain and Italy, on the other hand are closer to the

“blue” group of countries (Cluster 1), meaning that they have characteristics

similar to the countries situated in the center of the map. We observe that in the

center of the map we have mostly the economies from South America and from

Central Europe (Poland, Czech, Croatia, Slovenia) and a key characteristic, as seen

from Figure 5, is the increased current account deficit at macroeconomic level. A

subgroup of countries from the first cluster are more oriented to the right side of

the map, that is to the countries with the lowest economic development from the

sample. In this category we have the Baltic countries, Romania, Argentina,

Colombia, Bulgaria, Turkey. These are the countries where we also register a low

level of the development for the financial and moreover for the capital market. We

also highlight the large non-performing loans rate for Egypt, Tunisia and Ukraine,

while the top countries as for value added industry are situated at the top of the



_________________________________________________________________

map (China, Malaysia, Oman, Saudi Arabia). This is the “picture” of the worlds’

economies in the year preceding the global financial and economic crisis. In the

next section we will analyze the mutations produced among the economies in the

aftermath of the crisis.

5.3 Structural changes in the map at 2010

In this section of the paper we will analyze the self-organizing map in 2010, based

on the same inputs used for 2007 (sample was reduced with four countries due to

lack of data). In Figure 6 we have the topology of the economies on four distinct

groups.

Figure 6 – Self-Organizing Map of the economies in 2010

The first group includes the following countries (the “blue” group in Figure 6):

- Mexico, Colombia, El Salvador. - Poland, Slovenia, Czech Republic, Slovakia, Finland, Belgium, Austria,

Germany, France, Portugal, Ireland, Greece, Island, Malta, Italy, Romania,

Bulgaria, Hungary, Estonia, Croatia, Lithuania, Latvia, Macedonia, Serbia,

Bosnia and Herzegovina, Cyprus

- New Zeeland, Japan, Morocco, Jordan, Tunisia

Smaranda Cimpoeru

_________________________________________________________________ The main characteristic for this group of countries is the low level for the GDP

growth. The “red” group of countries is individualized by high levels of inflation,

money growth, agriculture value added and low levels of GDP/capita and Domestic

Credit. Based on this descriptions, we can conclude that these are the countries

which were the most affected by the Global crisis. Countries included in the “red”

group are:

- Bolivia, Peru, Uruguay, Argentina, Paraguay, Brazil. - Indonesia, India, Sri Lanka, Pakistan, Egypt, Turkey, Georgia, Russia,

Armenia, Ukraine, Moldova.

- Nigeria, Zambia, Cote d’Ivoire. On the right side of the map we find two sets of countries. Namely, the “yellow”

and the “green” group. The “yellow” countries have high values for the value

added in industry and for Savings. These countries are the following:

- Qatar, Oman, Saudi Arabia, Thailand, Philippine, Singapore, Korea, Malaysia.

- Norway, Chile, Trinidad Tobago. The last group of countries registers high values for the market capitalization,

Stocks traded, Domestic credit and for the GDP/capita. The countries in this group

are:

- Sweden, Denmark, Great Britain, Switzerland, Netherlands, Spain. - Canada, USA, Australia, South Africa.

In Figure 7 below, we can observe the distribution of the variables in 2010 for the

entire sample.

Figure 7 – Distribution of variables (U-Matrix) at 2010



_________________________________________________________________

6. Conclusions

In the present paper we have focused on two main objectives – observe the

way the major events in 2007 affected a whatsoever “stable” map of the economies

and focus on the key drivers that contributed to the overall performance of the

economies during the crisis period, that is delimiting some “early warning signs”

of crisis. We find that developed economies in the Western Europe have been as

vulnerable as the emerging ones, in terms of macroeconomic indicators

performance. The economies which that could be considered the less affected by

the global crisis are the Asian markets and some Northern Europe economies. This

result can be put on the account of the confidence in the financial markets of the

Asian economies, which confirms the importance of the financial stability in the

global economic environment.

The paper enriches the specialty literature of using self-organizing maps for

characterizing crisis situations, by adding significant insight into the changes that

took place on the “map” of economies after the global crisis from 2007, by

identifying main groups of countries, their particularities and the distribution on the

considered macroeconomic variables.

Smaranda Cimpoeru

_________________________________________________________________

Acknowledgments

This work was cofinanced from the European Social Fund through Sectoral

Operational Program Human Resources Development 2007-2013, project

number POSDRU/159/1.5/S/134197 „Performance and excellence in doctoral

and postdoctoral research in Romanian economics science domain”.

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